//编写一个程序，通过填充空格来解决数独问题。 
//
// 数独的解法需 遵循如下规则： 
//
// 
// 数字 1-9 在每一行只能出现一次。 
// 数字 1-9 在每一列只能出现一次。 
// 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图） 
// 
//
// 数独部分空格内已填入了数字，空白格用 '.' 表示。 
//
// 
//
// 
// 
// 
// 示例 1： 
//
// 
//输入：board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".
//",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".
//","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6
//"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[
//".",".",".",".","8",".",".","7","9"]]
//输出：[["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8
//"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],[
//"4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9",
//"6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4",
//"5","2","8","6","1","7","9"]]
//解释：输入的数独如上图所示，唯一有效的解决方案如下所示：
//
//
// 
//
// 
//
// 提示： 
//
// 
// board.length == 9 
// board[i].length == 9 
// board[i][j] 是一位数字或者 '.' 
// 题目数据 保证 输入数独仅有一个解 
// 
// 
// 
// 
// Related Topics 数组 回溯 矩阵 👍 1222 👎 0

package leetcode.editor.cn;

class SudokuSolver {
    public static void main(String[] args) {
        Solution solution = new SudokuSolver().new Solution();
    }

    //leetcode submit region begin(Prohibit modification and deletion)
    class Solution {
        public void solveSudoku(char[][] board) {
            if (board == null) {
                return;
            }
            backtracking(board);
        }

        public boolean backtracking(char[][] board) {
            // 可以不需要返回条件，不符合会返回false

            // 遍历整个二维数组
            for (int i = 0; i < board.length; i++) {
                for (int j = 0; j < board[0].length; j++) {
                    if (board[i][j] != '.') continue;   // 此时位置已经有数字，跳过
                    for (char k = '1'; k <= '9'; k++) {   // 依次判断数组 1~9
                        if (isValid(i, j, k, board)) {
                            board[i][j] = k;
                            if (backtracking(board)) return true;   // 找到一条就返回
                            board[i][j] = '.';
                        }
                    }
                    return false;   // 如果9个数字都不满足条件，那么此处此数独无解
                }
            }

            return true;    // 所有都遍历完没有返回false，满足条件
        }


        /**
         * 判断一行，一列，以及九宫格中是否有重复的数字
         *
         * @param row
         * @param col
         * @param val
         * @param board
         * @return
         */
        public boolean isValid(int row, int col, char val, char[][] board) {
            // 判断一行
            for (int i = 0; i < board[row].length; i++) {
                if (board[row][i] == val) {
                    return false;
                }
            }

            // 判断一列
            for (int i = 0; i < board.length; i++) {
                if (board[i][col] == val) {
                    return false;
                }
            }

            // 判断九宫格
            int startRow = (row / 3) * 3;  // 行起始位置
            int startCol = (col / 3) * 3;  // 列起始位置
            for (int i = startRow; i < startRow + 3; i++) {
                for (int j = startCol; j < startCol + 3; j++) {
                    if (board[i][j] == val) {
                        return false;
                    }
                }
            }

            return true;
        }

    }
//leetcode submit region end(Prohibit modification and deletion)

}
